New findings show that minimal feature diversity at neural network initialization is harmful but can be mitigated with noise.
problem The importance of feature diversity at neural network initialization.
method A series of experiments comparing different initialization schemes, including adding noise.
result Minimal feature diversity is harmful but can be mitigated with noise, even standard GPU noise is sufficient.
The paper develops a theory linking pretraining and fine-tuning in neural networks.
problem Understanding how initialization choices impact feature learning and generalization in neural networks.
method Analytical theory of diagonal linear networks, deriving generalization error as a function of initialization parameters and task statistics.
result Different initialization choices place networks into four fine-tuning regimes with varying abilities to support feature learning and generalization.
New method shows random, diverse initializations are not essential for deep neural networks.
problem The necessity of random, diverse initializations in deep neural networks.
method Constructed a deep convolutional network with identical features by initializing weights to 0, enabling signal propagation and stable gradients.
result Random, diverse initializations are not necessary for training neural networks.
Exact solutions reveal how unbalanced initializations promote rapid feature learning in neural networks.
problem Understanding how neural networks efficiently extract features from data.
method Deriving exact solutions to a minimal model of neural networks transitioning between lazy and rich learning regimes.
result Unbalanced layer-specific initialization variances and learning rates determine the degree of feature learning.
CatGCN improves GCNs by modeling feature interactions for categorical node features.
problem Suboptimal initial node representations in GCNs due to lack of feature interaction modeling.
method Integrates explicit interaction modeling (local and global) into initial node representation learning for categorical node features.
result CatGCN enhances initial node representations through feature interaction modeling, leading to improved model performance.
New method initializes MLPs for tabular data with tree-based feature interactions.
problem No dedicated neural network architecture for tabular data.
method Sparse tree-based initialization for MLPs.
result New method outperforms default MLP initialization and gradient boosting.
Graph neural networks benefit from node features but struggle with featureless graphs.
problem Graph neural networks struggle with featureless graphs.
method Analyzed node features' impact, proposed new feature initialization methods.
result Artificial features are highly competitive with real features.
This paper shows how deep neural networks can learn rich, independent features that significantly deviate from initialization.
problem Understanding how deep neural networks achieve meaningful feature learning and global convergence.
method Investigation of infinitely wide, L-layer neural networks using the tensor program framework under Maximal Update parametrization. result SGD enables these networks to learn linearly independent features that substantially deviate from their initial values, capturing relevant data information.
Gradient descent amplifies random features in neural networks to useful ones.
problem Generalization in neural networks trained on corrupted data.
method Characterization of feature-learning process in two-layer ReLU networks trained by gradient descent.
result Gradient descent amplifies random features to useful ones, achieving near optimal generalization error.
DISCERN estimates K for K-Means clustering efficiently.
problem Estimating the number of clusters in data.
method A deterministic initialization method for K-Means++.
result Improves both K estimation and clustering performance.
GNNs with random node initialization are shown to be universally expressive.
problem Limitations of standard GNNs in distinguishing graphs.
method Random node initialization (RNI) to enhance GNNs' expressive power.
result GNNs with RNI are proven to be universally expressive.
Grokking occurs when neural networks transition from lazy to rich training dynamics, fitting initial features before generalizing.
problem Understanding why neural networks exhibit early train loss decrease without corresponding test loss improvement.
method Analyzing vanilla gradient descent on polynomial regression with a two-layer neural network, identifying sufficient statistics for test loss.
result Grokking arises when a network first attempts to fit a kernel regression solution with initial features, followed by late-time feature learning.
Graph neural networks benefit from a new initialization method that improves node learning.
problem Poor initialization in GNNs leads to slower convergence and increased training instability.
method Integrates a statistically grounded one-hot graph encoder embedding (GEE) into standard GNNs.
result GG framework provides consistent and substantial performance gains in node classification.
ReLU neural networks define piecewise linear functions of their inputs. However, initializing and training a neural network is very different from fitting a linear spline. In this paper, we expand empirically upon previous theoretical work to demonstrate features of trained neural networks. Standard network initializat…
In machine learning, Feature Selection (FS) is a major part of efficient algorithm. It fuels the algorithm and is the starting block for our prediction. In this paper, we present a new method, called Optimal Coordinate Ascent (OCA) that allows us selecting features among block and individual features. OCA relies on coo…
An important research direction in machine learning has centered around developing meta-learning algorithms to tackle few-shot learning. An especially successful algorithm has been Model Agnostic Meta-Learning (MAML), a method that consists of two optimization loops, with the outer loop finding a meta-initialization, f…
LLT transforms time series features based on linear laws.
problem Classifying univariate and multivariate time series.
method Time-delay embedding, spectral decomposition, and feature transformation.
result Transformed features improve classification accuracy.
A new method averages neural network parameters to rank features robustly.
problem Neural networks' sensitivity to random initialization affects feature ranking robustness.
method Parameter averaging of multiple shallow networks trained with different random seeds.
result The averaged model discovers ground-truth feature importance consistently.
Large learning rates lead to optimal generalization if chosen carefully.
problem Understanding the optimal range of large learning rates for neural network training.
method Empirical study focusing on two questions: optimal initial LR range and differences between models trained with different LRs.
result Optimal initial learning rates slightly above the convergence threshold lead to optimal results after fine-tuning with a small LR or weight averaging.
Study on fluctuations in neural network kernels and predictions, focusing on finite width effects.
problem Characterizing fluctuations in finite width neural networks.
method Dynamical mean field theory analysis of wide but finite feature learning neural networks.
result Fluctuations in kernels and predictions are dynamically coupled, leading to reduced variance in feature learning regimes.
Graphs avoid oversmoothing with properly initialized weights.
problem Oversmoothing in graph convolutional networks (GCNs) limits their depth.
method Used Gaussian process equivalence to analyze GCNs, identifying a non-oversmoothing phase.
result Properly initialized GCNs can be deep and expressive.
This paper presents a phase diagram for two-layer neural networks under different initialization scales.
problem Understanding the behavior of neural networks under varying scales of initialization.
method Analysis of a phase diagram for two-layer neural networks.
result Condensation of weight vectors on isolated orientations during training.
The paper establishes principles for initializing and designing GNNs with ReLU activations to avoid oversmoothing and correlation collapse.
problem Oversmoothing and correlation collapse in deep ReLU GNNs.
method The paper derives and validates three principles for initialization and architecture selection in finite width graph neural networks with ReLU activations.
result Correct initialization, residual aggregation operators, and residual connections significantly improve early training dynamics in deep ReLU GNNs.
New method improves model robustness against adversarial attacks.
problem Adversarial attacks can deceive models trained with transfer learning.
method Noisy feature distillation method for random initialization.
result Models trained with random initialization are more robust to attacks.
One gradient step improves neural network feature learning by aligning weights with the teacher model.
problem Improving feature learning in neural networks through gradient descent.
method First gradient descent step on the first-layer parameters of a two-layer neural network.
result The first gradient update contains a rank-1 spike, leading to alignment with the teacher model.
Initial margin requirements are becoming an increasingly common feature of derivative markets. However, while the valuation of derivatives under collateralisation (Piterbarg 2010, Piterbarg2012), under counterparty risk with unsecured funding costs (FVA) (Burgard2011, Burgard2011, Burgard2013) and in the presence of re…
Model shows feature learning can improve neural scaling laws for hard tasks.
problem Understanding and improving neural network scaling laws for various task difficulties.
method Developed a solvable model of neural scaling laws, identified three scaling regimes, and demonstrated feature learning's impact on scaling exponents.
result Feature learning can improve scaling with training time and compute for hard tasks, nearly doubling the exponent.
The study analyzes transfer learning in infinite-width neural networks, improving generalization on target tasks.
problem Improving generalization in neural networks when using pretraining on a source task.
method Developed a theory under gradient flow for infinitely wide networks, analyzing fine-tuning and joint pretraining.
result Summary statistics of randomly initialized networks after pretraining are adaptive kernels that depend on both source and target data.
Combines geometric and topological info for complex object boundaries.
problem Boundary estimation for images with complex topologies.
method Topological clustering for initialization of Bayesian active contour model.
result Smart initialization reduces user dependence and improves accuracy.
Develops a tensor decomposition method with side information.
problem Identifying the relationship between a high-dimensional tensor and side information.
method Supervised tensor decomposition incorporating multiple feature matrices.
result Captures effective dimension reduction of the data tensor in feature space.
This work explores feature learning tradeoffs in neural networks.
problem Resource tradeoffs in neural feature learning.
method Theoretical and experimental investigation of offline sparse parity learning.
result Width improves sample efficiency in sparse feature learning.
Proves stability of Minkowski space for specific initial data.
problem Stability of Minkowski space under spacelike-characteristic initial data.
method Vectorfield method and bootstrapping argument, with new geometric constructions.
result Global nonlinear stability of Minkowski space proved for the spacelike-characteristic Cauchy problem.
Grassmannian packings improve CNN kernels' diversity and reduce sparsity.
problem Kernel sparsity and lack of diversity in CNNs decrease model capacity.
method Initialize CNN kernels with Grassmannian packings to maximize diversity and minimize sparsity.
result Grassmannian packings lead to diverse features and improved classification accuracy.
Novel bounds for logistic regression coreset construction and feature selection.
problem Efficiently summarize and reduce logistic regression inputs.
method Feature space sketching for logistic regression.
result Tight bounds for coreset construction and feature selection.
AGF explains feature learning in neural networks through alternating steps.
problem Understanding what features neural networks learn and how they learn them.
method AGF is an algorithmic framework that approximates the dynamics of feature learning in two-layer networks.
result AGF provides a unified framework to understand feature learning in neural networks, matching experimental results across various architectures.
New method removes contrastive loss by adding a prediction head, revealing learning mechanisms.
problem Understanding why neural networks learn competitive representations despite trivial optima.
method Empirical and theoretical analysis of a trainable, identity-initialized prediction head.
result The trainable prediction head enables learning all features, preventing dimensional collapse.
Hyperparameter optimization aims to find the optimal hyperparameter configuration of a machine learning model, which provides the best performance on a validation dataset. Manual search usually leads to get stuck in a local hyperparameter configuration, and heavily depends on human intuition and experience. A simple al…
FINs enhance performance in diverse datasets like finance, speech, and health.
problem Improving neural network performance across various domains.
method Feature Imitating Networks (FINs) initialize weights to approximate specific statistical features.
result FINs significantly improve performance in Bitcoin price prediction, speech emotion recognition, and chronic neck pain detection.
Memory-Augmented Meta-Optimization improves cold-start recommendation.
problem Cold-start problem in recommender systems for new users or items.
method Memory-Augmented Meta-Optimization approach with personalized and task-specific memories.
result Significant improvement in cold-start recommendation performance on multiple datasets.
Random feature models approximate functions in Banach spaces efficiently.
problem Approximating functions in Banach spaces efficiently.
method Randomly initialized feature maps and linear readout training.
result Universal approximation in Bochner spaces for Banach space-valued models.
A new text clustering method using NMF and LSA improves stability and performance.
problem Text data's large, sparse term-document matrix makes clustering difficult.
method Proposes a new feature agglomeration method based on NMF and deterministic K-Means initialization.
result Significantly improves clustering performance and stability.
A problem of paramount importance in both pure (Restricted Invertibility problem) and applied mathematics (Feature extraction) is the one of selecting a submatrix of a given matrix, such that this submatrix has its smallest singular value above a specified level. Such problems can be addressed using perturbation analys…
Deep networks with orthogonal weights show stable fluctuations, improving generalization and training speed.
problem Fluctuations in deep networks with Gaussian weights can impair training, especially in networks with depth comparable to width.
method Analytical and numerical studies of fully-connected networks with orthogonal weight initialization and tanh activations.
result Rectangular networks with orthogonal weights have stable fluctuations independent of network depth, leading to better generalization and training speed.
Study shows neural networks learn low frequencies first, proposing solutions.
problem Frequency bias in neural network learning process.
method Developed a PDE to unravel frequency dynamics, used Fourier Features model.
result Appropriate weight initialization can eliminate or control frequency bias.
SGD batch size affects autoencoder global minima sparsity and sharpness.
problem Investigating how batch size impacts autoencoder learning.
method Non-convex autoencoder training with SGD, varying batch sizes.
result SGD batch size influences global minimum sparsity and sharpness.
Two distinct limits for deep learning have been derived as the network width h→∞, depending on how the weights of the last layer scale with h. In the Neural Tangent Kernel (NTK) limit, the dynamics becomes linear in the weights and is described by a frozen kernel Θ. By contrast, in the Mean-Field …
Deep learning models can have low bias and variance, contrary to classical theory.
problem Understanding the performance of deep learning models at high complexity.
method Developed a fine-grained bias-variance decomposition for random feature kernel regression, analyzing the effects of sampling, initialization, and labels.
result The variance terms exhibit non-monotonic behavior and can diverge at the interpolation boundary, even in the absence of label noise.
Framework explains how dual deep networks learn features from unlabeled data.
problem Understanding self-supervised learning with dual deep networks.
method Theoretical framework and hierarchical latent tree model.
result Deep ReLU networks learn latent variables through contrastive SSL.